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Fulton, who took over from Craig McMillan after the 2019 World Cup, will become Canterbury's new head coach; returning to a province for whom he played 16 seasons and 315 matches.
Under his tenure, the Black Caps batsmen performed strongly in test series victories over England and India, but came in for criticism after a disastrous Australian test tour in which their highest score was 256. In the shorter formats, Super Over struggles continued with some shaky death batting in Twenty20 showdowns, but a 3-0 sweep of India proved the New Zealand batsmen remained one of the world's best one-day units.
Formerly a batting coach for the New Zealand Under-19s and assistant with Canterbury, Fulton said his decision was a result of wanting to begin his head coaching career, while also spending more time with his family.
"I've always wanted to be a head coach with the added roles and responsibilities that come with the job," said the 41-year-old.
"To get the chance to do it for a province I'm passionate about and to be home with my young family made it the perfect job."
Canterbury haven't claimed a provincial title since doing the four-day and one-day double in the 2016-17 season, and Fulton believes that goal goes hand-in-hand with his aspiration to develop players to the point where they can join the environment he is departing.
"There are guys there that have the potential to play international cricket and my job is to get them there," Fulton said.
"If those guys can make the step up to international cricket, then I'm sure Canterbury will have some success along the way."
Fulton takes over at Canterbury on August 1, and with the Black Caps having not played since March and unlikely to be back in action until November due to the effects of the Covid-19 pandemic, New Zealand Cricket high performance general manager Bryan Stronach says there will be no rush to fill Fulton's role.
"With the Black Caps entering a winter period at home we'll take some time to consider our options in terms of a replacement for Pete."